From: Merv Bitikofer <mrb22667@kansas.net>

Date: Wed Apr 08 2009 - 08:13:48 EDT

Date: Wed Apr 08 2009 - 08:13:48 EDT

Thanks, George --this was helpful to correct my misunderstanding of

this. If I read you (or Planck) correctly below, it would be more

correct to say that the "linear thinking" that we apply so well to our

Macro world breaks down even for time and space in the [extreme]

micro-world --but that is not the same as proving some discrete

"smallest increment of space." & in any case, no mechanical thing

could make any meaningful measurements in that scale since time & space

itself (at that precision) would be warped by the presence of the

mechanical measuring device. If any of this is still glaringly wrong,

your further patience and correction is appreciated. It still feels

like a trip down the rabbit-hole, but at least I can have my continuous

space-time back for the moment!

--Merv

George Murphy wrote:

*> Merv -
*

*>
*

*> Actually Planck himself, in the paper in which he introduced "his"
*

*> constant h, pointed out that it, together with the speed of light c
*

*> and gravitational constant G, defined a natural system of length, time
*

*> & mass units:
*

*>
*

*> L = sqrt(hG/c^3) ~ 10^-33 cm, T = L/c ~ 10^-43sec , M = Lc^2/G ~
*

*> 10^-5gm.
*

*>
*

*> (h there is Planck's h over 2*pi.) But this is simply dimensional
*

*> analysis & doesn't mean that you can't actually have lengths or times
*

*> smaller than L & T. The best way to show that clearly is as follows.
*

*> (This follows a paper of mine in American Journal of Physics 42, 1974,
*

*> p.958.)
*

*>
*

*> The quantum mechanical uncertainty principle says measurement of a
*

*> time interval t will be related to the uncertainty in the energy of
*

*> the system DE by t*DE > h .
*

*> In addition, the gravitational field of the clock will, according to
*

*> general relativity, influence the rate at which the clock runs. The
*

*> fractional change in an interval t in the vicinity of the clock will
*

*> be on the order of dt/t ~ gravitational potential/c^2 ~ G[M +
*

*> DE/c^2]/Lc^2, where M is the clock's mass, L its linear dimension, and
*

*> the uncertainty in energy gives an uncertainty in mass according to
*

*> Einstein's formula.
*

*>
*

*> Now in order for the clock to measure an interval t its parts must be
*

*> able to communicate with one another within that time, so L < ct.
*

*> Thus dt/t >
*

*> G[M + DE/c^2]/c^3 > GDE/c^5 . But since DE > h/t we have dt >
*

*> Gh/tc^5. The measurement is of no value unless dt < t - i.e., unless
*

*> t > sgrt(hG/c^5), the Planck time defined above.
*

*>
*

*> This does not mean, however, that space-time is quantized in the sense
*

*> that there are "atoms" of space & time. That may be the case but all
*

*> this argument shows is that the the concepts of length & time
*

*> intervals lose their meaning below the Planck scale. There are
*

*> reasons to think that space-time is still continuous, but it is not a
*

*> metric space below this scale.
*

*>
*

*> Shalom
*

*> George
*

*> http://home.roadrunner.com/~scitheologyglm
*

*>
*

*> ----- Original Message ----- From: <mrb22667@kansas.net>
*

*> To: "asa" <asa@calvin.edu>
*

*> Sent: Tuesday, April 07, 2009 5:14 PM
*

*> Subject: [asa] planck for the layman?
*

*>
*

*>
*

*>>
*

*>> I'm needing help understanding some of the apparent ramifications
*

*>> that come from
*

*>> Planck's constant ... such as: somehow a quantized packet of energy
*

*>> leads to a
*

*>> "smallest packet" of space? --and of time as well? I think I
*

*>> remember this from
*

*>> a previous ASA discussion, but didn't understand it at the time &
*

*>> still don't now.
*

*>>
*

*>> Does this effectively cap our logarithmic romp towards smaller things
*

*>> in much
*

*>> the same way as Einstein's still expanding space caps the "think-big"
*

*>> end?
*

*>> If there is a good book on Planck for the layman, let me know.
*

*>>
*

*>> --Merv
*

*>> (It's enough to give a Euclidean-minded geometry teacher a headache.)
*

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Received on Wed Apr 8 08:14:04 2009

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